Determine the intercepts of the line. $ 4x-3y=17$ $y$ -intercept: $\Big($
Answer: The $y$ -intercept of a graph is the point of intersection between the $y$ -axis and the graph. Since the $y$ -axis is also the line $x=0$, the $x$ -value of this point will always be $0$. The $x$ -intercept of a graph is the point of intersection between the $x$ -axis and the graph. Since the $x$ -axis is also the line $y=0$, the $y$ -value of this point will always be $0$. To find the $y$ -intercept, let's substitute $ x= 0$ into the equation and solve for $y$ : $\begin{aligned}4\cdot{0}-3y&=17\\ -3y&=17\\ y&=-\dfrac{17}{3}\end{aligned}$ So the $y$ -intercept is $\left(0,-\dfrac{17}{3}\right)$. To find the $x$ -intercept, let's substitute $ y= 0$ into the equation and solve for $x$ : $\begin{aligned}4x-3\cdot{0}&=17\\ 4x&=17\\ x&=\dfrac{17}{4}\end{aligned}$ So the $x$ -intercept is $\left(\dfrac{17}{4},0\right)$. In conclusion, The $y$ -intercept is $\left(0,-\dfrac{17}{3}\right)$. The $x$ -intercept is $\left(\dfrac{17}{4},0\right)$.